# Step-by-step Solution

Go!
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$

Solving method

Learn how to solve product rule of differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)\sqrt{x^2-1}+x\frac{d}{dx}\left(\sqrt{x^2-1}\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(x(x^2-1)^0.5). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{x^2-1}. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two functions is the sum of the derivatives of each function.

## Final Answer

$\frac{-1+2x^2}{\sqrt{x^2-1}}$
SnapXam A2
Answer Assistant

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5
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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Tips on how to improve your answer:

$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$

### Main topic:

Product Rule of differentiation

~ 0.87 s